(x-4)(2x+3)=(3x-12)(5x-7)

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Solution for (x-4)(2x+3)=(3x-12)(5x-7) equation: 


Simplifying
(x + -4)(2x + 3) = (3x + -12)(5x + -7)

Reorder the terms:
(-4 + x)(2x + 3) = (3x + -12)(5x + -7)

Reorder the terms:
(-4 + x)(3 + 2x) = (3x + -12)(5x + -7)

Multiply (-4 + x) * (3 + 2x)
(-4(3 + 2x) + x(3 + 2x)) = (3x + -12)(5x + -7)
((3 * -4 + 2x * -4) + x(3 + 2x)) = (3x + -12)(5x + -7)
((-12 + -8x) + x(3 + 2x)) = (3x + -12)(5x + -7)
(-12 + -8x + (3 * x + 2x * x)) = (3x + -12)(5x + -7)
(-12 + -8x + (3x + 2x2)) = (3x + -12)(5x + -7)

Combine like terms: -8x + 3x = -5x
(-12 + -5x + 2x2) = (3x + -12)(5x + -7)

Reorder the terms:
-12 + -5x + 2x2 = (-12 + 3x)(5x + -7)

Reorder the terms:
-12 + -5x + 2x2 = (-12 + 3x)(-7 + 5x)

Multiply (-12 + 3x) * (-7 + 5x)
-12 + -5x + 2x2 = (-12(-7 + 5x) + 3x * (-7 + 5x))
-12 + -5x + 2x2 = ((-7 * -12 + 5x * -12) + 3x * (-7 + 5x))
-12 + -5x + 2x2 = ((84 + -60x) + 3x * (-7 + 5x))
-12 + -5x + 2x2 = (84 + -60x + (-7 * 3x + 5x * 3x))
-12 + -5x + 2x2 = (84 + -60x + (-21x + 15x2))

Combine like terms: -60x + -21x = -81x
-12 + -5x + 2x2 = (84 + -81x + 15x2)

Solving
-12 + -5x + 2x2 = 84 + -81x + 15x2

Solving for variable 'x'.

Reorder the terms:
-12 + -84 + -5x + 81x + 2x2 + -15x2 = 84 + -81x + 15x2 + -84 + 81x + -15x2

Combine like terms: -12 + -84 = -96
-96 + -5x + 81x + 2x2 + -15x2 = 84 + -81x + 15x2 + -84 + 81x + -15x2

Combine like terms: -5x + 81x = 76x
-96 + 76x + 2x2 + -15x2 = 84 + -81x + 15x2 + -84 + 81x + -15x2

Combine like terms: 2x2 + -15x2 = -13x2
-96 + 76x + -13x2 = 84 + -81x + 15x2 + -84 + 81x + -15x2

Reorder the terms:
-96 + 76x + -13x2 = 84 + -84 + -81x + 81x + 15x2 + -15x2

Combine like terms: 84 + -84 = 0
-96 + 76x + -13x2 = 0 + -81x + 81x + 15x2 + -15x2
-96 + 76x + -13x2 = -81x + 81x + 15x2 + -15x2

Combine like terms: -81x + 81x = 0
-96 + 76x + -13x2 = 0 + 15x2 + -15x2
-96 + 76x + -13x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-96 + 76x + -13x2 = 0

Factor a trinomial.
(-4 + x)(24 + -13x) = 0


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(24 + -13x)' equal to zero and attempt to solve:

Simplifying
24 + -13x = 0

Solving
24 + -13x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -13x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -13x = 0 + -24
-13x = 0 + -24

Combine like terms: 0 + -24 = -24
-13x = -24

Divide each side by '-13'.
x = 1.846153846

Simplifying
x = 1.846153846
Solution
x = {4, 1.846153846}

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