(5x+45)(3x-25)=180

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Solution for (5x+45)(3x-25)=180 equation: 


Simplifying
(5x + 45)(3x + -25) = 180

Reorder the terms:
(45 + 5x)(3x + -25) = 180

Reorder the terms:
(45 + 5x)(-25 + 3x) = 180

Multiply (45 + 5x) * (-25 + 3x)
(45(-25 + 3x) + 5x * (-25 + 3x)) = 180
((-25 * 45 + 3x * 45) + 5x * (-25 + 3x)) = 180
((-1125 + 135x) + 5x * (-25 + 3x)) = 180
(-1125 + 135x + (-25 * 5x + 3x * 5x)) = 180
(-1125 + 135x + (-125x + 15x2)) = 180

Combine like terms: 135x + -125x = 10x
(-1125 + 10x + 15x2) = 180

Solving
-1125 + 10x + 15x2 = 180

Solving for variable 'x'.

Reorder the terms:
-1125 + -180 + 10x + 15x2 = 180 + -180

Combine like terms: -1125 + -180 = -1305
-1305 + 10x + 15x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-1305 + 10x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-261 + 2x + 3x2) = 0

Factor a trinomial.
5((-29 + -3x)(9 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-29 + -3x)' equal to zero and attempt to solve:

Simplifying
-29 + -3x = 0

Solving
-29 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '29' to each side of the equation.
-29 + 29 + -3x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -3x = 0 + 29
-3x = 0 + 29

Combine like terms: 0 + 29 = 29
-3x = 29

Divide each side by '-3'.
x = -9.666666667

Simplifying
x = -9.666666667

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-9.666666667, 9}

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