(x-4)(2x+3)=4(x-1)-12

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Solution for (x-4)(2x+3)=4(x-1)-12 equation:


Simplifying
(x + -4)(2x + 3) = 4(x + -1) + -12

Reorder the terms:
(-4 + x)(2x + 3) = 4(x + -1) + -12

Reorder the terms:
(-4 + x)(3 + 2x) = 4(x + -1) + -12

Multiply (-4 + x) * (3 + 2x)
(-4(3 + 2x) + x(3 + 2x)) = 4(x + -1) + -12
((3 * -4 + 2x * -4) + x(3 + 2x)) = 4(x + -1) + -12
((-12 + -8x) + x(3 + 2x)) = 4(x + -1) + -12
(-12 + -8x + (3 * x + 2x * x)) = 4(x + -1) + -12
(-12 + -8x + (3x + 2x2)) = 4(x + -1) + -12

Combine like terms: -8x + 3x = -5x
(-12 + -5x + 2x2) = 4(x + -1) + -12

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

Reorder the terms:
-12 + -5x + 2x2 = -4 + -12 + 4x

Combine like terms: -4 + -12 = -16
-12 + -5x + 2x2 = -16 + 4x

Solving
-12 + -5x + 2x2 = -16 + 4x

Solving for variable 'x'.

Reorder the terms:
-12 + 16 + -5x + -4x + 2x2 = -16 + 4x + 16 + -4x

Combine like terms: -12 + 16 = 4
4 + -5x + -4x + 2x2 = -16 + 4x + 16 + -4x

Combine like terms: -5x + -4x = -9x
4 + -9x + 2x2 = -16 + 4x + 16 + -4x

Reorder the terms:
4 + -9x + 2x2 = -16 + 16 + 4x + -4x

Combine like terms: -16 + 16 = 0
4 + -9x + 2x2 = 0 + 4x + -4x
4 + -9x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
4 + -9x + 2x2 = 0

Factor a trinomial.
(1 + -2x)(4 + -1x) = 0

Subproblem 1

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {0.5, 4}

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