5(2x-7)(5x+6)=0

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Solution for 5(2x-7)(5x+6)=0 equation: 


Simplifying
5(2x + -7)(5x + 6) = 0

Reorder the terms:
5(-7 + 2x)(5x + 6) = 0

Reorder the terms:
5(-7 + 2x)(6 + 5x) = 0

Multiply (-7 + 2x) * (6 + 5x)
5(-7(6 + 5x) + 2x * (6 + 5x)) = 0
5((6 * -7 + 5x * -7) + 2x * (6 + 5x)) = 0
5((-42 + -35x) + 2x * (6 + 5x)) = 0
5(-42 + -35x + (6 * 2x + 5x * 2x)) = 0
5(-42 + -35x + (12x + 10x2)) = 0

Combine like terms: -35x + 12x = -23x
5(-42 + -23x + 10x2) = 0
(-42 * 5 + -23x * 5 + 10x2 * 5) = 0
(-210 + -115x + 50x2) = 0

Solving
-210 + -115x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-42 + -23x + 10x2) = 0

Factor a trinomial.
5((-6 + -5x)(7 + -2x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = 0 + 6
-5x = 0 + 6

Combine like terms: 0 + 6 = 6
-5x = 6

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2

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
Solution
x = {-1.2, 3.5}

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