2(4x+3)2(2x-4)=0

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Solution for 2(4x+3)2(2x-4)=0 equation: 


Simplifying
2(4x + 3) * 2(2x + -4) = 0

Reorder the terms:
2(3 + 4x) * 2(2x + -4) = 0

Reorder the terms:
2(3 + 4x) * 2(-4 + 2x) = 0

Reorder the terms for easier multiplication:
2 * 2(3 + 4x)(-4 + 2x) = 0

Multiply 2 * 2
4(3 + 4x)(-4 + 2x) = 0

Multiply (3 + 4x) * (-4 + 2x)
4(3(-4 + 2x) + 4x * (-4 + 2x)) = 0
4((-4 * 3 + 2x * 3) + 4x * (-4 + 2x)) = 0
4((-12 + 6x) + 4x * (-4 + 2x)) = 0
4(-12 + 6x + (-4 * 4x + 2x * 4x)) = 0
4(-12 + 6x + (-16x + 8x2)) = 0

Combine like terms: 6x + -16x = -10x
4(-12 + -10x + 8x2) = 0
(-12 * 4 + -10x * 4 + 8x2 * 4) = 0
(-48 + -40x + 32x2) = 0

Solving
-48 + -40x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + -5x + 4x2) = 0

Factor a trinomial.
8((-3 + -4x)(2 + -1x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.75, 2}

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