4(2x-7)(6x+5)=0

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Solution for 4(2x-7)(6x+5)=0 equation: 


Simplifying
4(2x + -7)(6x + 5) = 0

Reorder the terms:
4(-7 + 2x)(6x + 5) = 0

Reorder the terms:
4(-7 + 2x)(5 + 6x) = 0

Multiply (-7 + 2x) * (5 + 6x)
4(-7(5 + 6x) + 2x * (5 + 6x)) = 0
4((5 * -7 + 6x * -7) + 2x * (5 + 6x)) = 0
4((-35 + -42x) + 2x * (5 + 6x)) = 0
4(-35 + -42x + (5 * 2x + 6x * 2x)) = 0
4(-35 + -42x + (10x + 12x2)) = 0

Combine like terms: -42x + 10x = -32x
4(-35 + -32x + 12x2) = 0
(-35 * 4 + -32x * 4 + 12x2 * 4) = 0
(-140 + -128x + 48x2) = 0

Solving
-140 + -128x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + -32x + 12x2) = 0

Factor a trinomial.
4((-5 + -6x)(7 + -2x)) = 0

Ignore the factor 4.

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

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 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 + -6x = 0 + 5

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

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

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

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 = {-0.8333333333, 3.5}

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