(3x-45)(4x+36)=0

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Solution for (3x-45)(4x+36)=0 equation: 


Simplifying
(3x + -45)(4x + 36) = 0

Reorder the terms:
(-45 + 3x)(4x + 36) = 0

Reorder the terms:
(-45 + 3x)(36 + 4x) = 0

Multiply (-45 + 3x) * (36 + 4x)
(-45(36 + 4x) + 3x * (36 + 4x)) = 0
((36 * -45 + 4x * -45) + 3x * (36 + 4x)) = 0
((-1620 + -180x) + 3x * (36 + 4x)) = 0
(-1620 + -180x + (36 * 3x + 4x * 3x)) = 0
(-1620 + -180x + (108x + 12x2)) = 0

Combine like terms: -180x + 108x = -72x
(-1620 + -72x + 12x2) = 0

Solving
-1620 + -72x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-135 + -6x + x2) = 0

Factor a trinomial.
12((-9 + -1x)(15 + -1x)) = 0

Ignore the factor 12.

Subproblem 1
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

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-9, 15}

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