5x(4x-12)-(2x-7)(4x-12)=0

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Solution for 5x(4x-12)-(2x-7)(4x-12)=0 equation:


Simplifying
5x(4x + -12) + -1(2x + -7)(4x + -12) = 0

Reorder the terms:
5x(-12 + 4x) + -1(2x + -7)(4x + -12) = 0
(-12 * 5x + 4x * 5x) + -1(2x + -7)(4x + -12) = 0
(-60x + 20x2) + -1(2x + -7)(4x + -12) = 0

Reorder the terms:
-60x + 20x2 + -1(-7 + 2x)(4x + -12) = 0

Reorder the terms:
-60x + 20x2 + -1(-7 + 2x)(-12 + 4x) = 0

Multiply (-7 + 2x) * (-12 + 4x)
-60x + 20x2 + -1(-7(-12 + 4x) + 2x * (-12 + 4x)) = 0
-60x + 20x2 + -1((-12 * -7 + 4x * -7) + 2x * (-12 + 4x)) = 0
-60x + 20x2 + -1((84 + -28x) + 2x * (-12 + 4x)) = 0
-60x + 20x2 + -1(84 + -28x + (-12 * 2x + 4x * 2x)) = 0
-60x + 20x2 + -1(84 + -28x + (-24x + 8x2)) = 0

Combine like terms: -28x + -24x = -52x
-60x + 20x2 + -1(84 + -52x + 8x2) = 0
-60x + 20x2 + (84 * -1 + -52x * -1 + 8x2 * -1) = 0
-60x + 20x2 + (-84 + 52x + -8x2) = 0

Reorder the terms:
-84 + -60x + 52x + 20x2 + -8x2 = 0

Combine like terms: -60x + 52x = -8x
-84 + -8x + 20x2 + -8x2 = 0

Combine like terms: 20x2 + -8x2 = 12x2
-84 + -8x + 12x2 = 0

Solving
-84 + -8x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + -2x + 3x2) = 0

Factor a trinomial.
4((-7 + -3x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 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 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2.333333333, 3}

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