(3x+4)(x-4)=9x+12

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Solution for (3x+4)(x-4)=9x+12 equation:


Simplifying
(3x + 4)(x + -4) = 9x + 12

Reorder the terms:
(4 + 3x)(x + -4) = 9x + 12

Reorder the terms:
(4 + 3x)(-4 + x) = 9x + 12

Multiply (4 + 3x) * (-4 + x)
(4(-4 + x) + 3x * (-4 + x)) = 9x + 12
((-4 * 4 + x * 4) + 3x * (-4 + x)) = 9x + 12
((-16 + 4x) + 3x * (-4 + x)) = 9x + 12
(-16 + 4x + (-4 * 3x + x * 3x)) = 9x + 12
(-16 + 4x + (-12x + 3x2)) = 9x + 12

Combine like terms: 4x + -12x = -8x
(-16 + -8x + 3x2) = 9x + 12

Reorder the terms:
-16 + -8x + 3x2 = 12 + 9x

Solving
-16 + -8x + 3x2 = 12 + 9x

Solving for variable 'x'.

Reorder the terms:
-16 + -12 + -8x + -9x + 3x2 = 12 + 9x + -12 + -9x

Combine like terms: -16 + -12 = -28
-28 + -8x + -9x + 3x2 = 12 + 9x + -12 + -9x

Combine like terms: -8x + -9x = -17x
-28 + -17x + 3x2 = 12 + 9x + -12 + -9x

Reorder the terms:
-28 + -17x + 3x2 = 12 + -12 + 9x + -9x

Combine like terms: 12 + -12 = 0
-28 + -17x + 3x2 = 0 + 9x + -9x
-28 + -17x + 3x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-28 + -17x + 3x2 = 0

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

Subproblem 1

Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-1.333333333, 7}

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