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

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


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

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

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

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

Combine like terms: -4x + 12x = 8x
(-6 + 8x + 8x2) = 0

Solving
-6 + 8x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4x + 4x2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

x = {-1.5, 0.5}

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