(3x+4)(8x-12)=0

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Solution for (3x+4)(8x-12)=0 equation:


Simplifying
(3x + 4)(8x + -12) = 0

Reorder the terms:
(4 + 3x)(8x + -12) = 0

Reorder the terms:
(4 + 3x)(-12 + 8x) = 0

Multiply (4 + 3x) * (-12 + 8x)
(4(-12 + 8x) + 3x * (-12 + 8x)) = 0
((-12 * 4 + 8x * 4) + 3x * (-12 + 8x)) = 0
((-48 + 32x) + 3x * (-12 + 8x)) = 0
(-48 + 32x + (-12 * 3x + 8x * 3x)) = 0
(-48 + 32x + (-36x + 24x2)) = 0

Combine like terms: 32x + -36x = -4x
(-48 + -4x + 24x2) = 0

Solving
-48 + -4x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -1x + 6x2) = 0

Factor a trinomial.
4((-4 + -3x)(3 + -2x)) = 0

Ignore the factor 4.

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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {-1.333333333, 1.5}

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