# Solve for x (3x-11)(2x+9)^2x=180

(3x-11)(2x+9)2x=180
Simplify (3x-11)(2x+9)2x.
Rewrite (2x+9)2 as (2x+9)(2x+9).
(3x-11)((2x+9)(2x+9))x=180
Expand (2x+9)(2x+9) using the FOIL Method.
Apply the distributive property.
(3x-11)(2x(2x+9)+9(2x+9))x=180
Apply the distributive property.
(3x-11)(2x(2x)+2x⋅9+9(2x+9))x=180
Apply the distributive property.
(3x-11)(2x(2x)+2x⋅9+9(2x)+9⋅9)x=180
(3x-11)(2x(2x)+2x⋅9+9(2x)+9⋅9)x=180
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
(3x-11)(2⋅2×2+2x⋅9+9(2x)+9⋅9)x=180
Multiply 2 by 2.
(3x-11)(4×2+2x⋅9+9(2x)+9⋅9)x=180
Multiply 9 by 2.
(3x-11)(4×2+18x+9(2x)+9⋅9)x=180
Multiply 2 by 9.
(3x-11)(4×2+18x+18x+9⋅9)x=180
Multiply 9 by 9.
(3x-11)(4×2+18x+18x+81)x=180
(3x-11)(4×2+18x+18x+81)x=180
(3x-11)(4×2+36x+81)x=180
(3x-11)(4×2+36x+81)x=180
Expand (3x-11)(4×2+36x+81) by multiplying each term in the first expression by each term in the second expression.
(3x(4×2)+3x(36x)+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
Simplify terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
(3⋅4(x⋅x2)+3x(36x)+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
Multiply x by x2 by adding the exponents.
Multiply x by x2.
Raise x to the power of 1.
(3⋅4(x1x2)+3x(36x)+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
Use the power rule aman=am+n to combine exponents.
(3⋅4×1+2+3x(36x)+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
(3⋅4×1+2+3x(36x)+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
(3⋅4×3+3x(36x)+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
(3⋅4×3+3x(36x)+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
Multiply 3 by 4.
(12×3+3x(36x)+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
Multiply x by x.
(12×3+3⋅36×2+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
Multiply 3 by 36.
(12×3+108×2+3x⋅81-11(4×2)-11(36x)-11⋅81)x=180
Multiply 81 by 3.
(12×3+108×2+243x-11(4×2)-11(36x)-11⋅81)x=180
Multiply 4 by -11.
(12×3+108×2+243x-44×2-11(36x)-11⋅81)x=180
Multiply 36 by -11.
(12×3+108×2+243x-44×2-396x-11⋅81)x=180
Multiply -11 by 81.
(12×3+108×2+243x-44×2-396x-891)x=180
(12×3+108×2+243x-44×2-396x-891)x=180
Simplify terms.
Subtract 44×2 from 108×2.
(12×3+64×2+243x-396x-891)x=180
Subtract 396x from 243x.
(12×3+64×2-153x-891)x=180
Apply the distributive property.
12x3x+64x2x-153x⋅x-891x=180
12x3x+64x2x-153x⋅x-891x=180
12x3x+64x2x-153x⋅x-891x=180
Simplify.
Multiply x3 by x by adding the exponents.
Move x.
12(x⋅x3)+64x2x-153x⋅x-891x=180
Multiply x by x3.
Raise x to the power of 1.
12(x1x3)+64x2x-153x⋅x-891x=180
Use the power rule aman=am+n to combine exponents.
12×1+3+64x2x-153x⋅x-891x=180
12×1+3+64x2x-153x⋅x-891x=180
12×4+64x2x-153x⋅x-891x=180
12×4+64x2x-153x⋅x-891x=180
Multiply x2 by x by adding the exponents.
Move x.
12×4+64(x⋅x2)-153x⋅x-891x=180
Multiply x by x2.
Raise x to the power of 1.
12×4+64(x1x2)-153x⋅x-891x=180
Use the power rule aman=am+n to combine exponents.
12×4+64×1+2-153x⋅x-891x=180
12×4+64×1+2-153x⋅x-891x=180
12×4+64×3-153x⋅x-891x=180
12×4+64×3-153x⋅x-891x=180
Multiply x by x by adding the exponents.
Move x.
12×4+64×3-153(x⋅x)-891x=180
Multiply x by x.
12×4+64×3-153×2-891x=180
12×4+64×3-153×2-891x=180
12×4+64×3-153×2-891x=180
12×4+64×3-153×2-891x=180
Graph each side of the equation. The solution is the x-value of the point of intersection.
x≈-5.08093716,-3.76829935,-0.21025244,3.72615563
Solve for x (3x-11)(2x+9)^2x=180