4x(5x-36)x(2x+7)=0

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Solution for 4x(5x-36)x(2x+7)=0 equation: 


Simplifying
4x(5x + -36) * x(2x + 7) = 0

Reorder the terms:
4x(-36 + 5x) * x(2x + 7) = 0

Reorder the terms:
4x(-36 + 5x) * x(7 + 2x) = 0

Reorder the terms for easier multiplication:
4x * x(-36 + 5x)(7 + 2x) = 0

Multiply x * x
4x2(-36 + 5x)(7 + 2x) = 0

Multiply (-36 + 5x) * (7 + 2x)
4x2(-36(7 + 2x) + 5x * (7 + 2x)) = 0
4x2((7 * -36 + 2x * -36) + 5x * (7 + 2x)) = 0
4x2((-252 + -72x) + 5x * (7 + 2x)) = 0
4x2(-252 + -72x + (7 * 5x + 2x * 5x)) = 0
4x2(-252 + -72x + (35x + 10x2)) = 0

Combine like terms: -72x + 35x = -37x
4x2(-252 + -37x + 10x2) = 0
(-252 * 4x2 + -37x * 4x2 + 10x2 * 4x2) = 0
(-1008x2 + -148x3 + 40x4) = 0

Solving
-1008x2 + -148x3 + 40x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(-252 + -37x + 10x2) = 0

Factor a trinomial.
4x2((-7 + -2x)(36 + -5x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 3
Set the factor '(36 + -5x)' equal to zero and attempt to solve:

Simplifying
36 + -5x = 0

Solving
36 + -5x = 0

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

Add '-36' to each side of the equation.
36 + -36 + -5x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -5x = 0 + -36
-5x = 0 + -36

Combine like terms: 0 + -36 = -36
-5x = -36

Divide each side by '-5'.
x = 7.2

Simplifying
x = 7.2
Solution
x = {0, -3.5, 7.2}

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