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

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


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

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

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

Multiply (-7 + 6x) * (5 + 2x)
5(-7(5 + 2x) + 6x * (5 + 2x)) = 0
5((5 * -7 + 2x * -7) + 6x * (5 + 2x)) = 0
5((-35 + -14x) + 6x * (5 + 2x)) = 0
5(-35 + -14x + (5 * 6x + 2x * 6x)) = 0
5(-35 + -14x + (30x + 12x2)) = 0

Combine like terms: -14x + 30x = 16x
5(-35 + 16x + 12x2) = 0
(-35 * 5 + 16x * 5 + 12x2 * 5) = 0
(-175 + 80x + 60x2) = 0

Solving
-175 + 80x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-35 + 16x + 12x2) = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-2.5, 1.166666667}

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