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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