(2x+4)(2x+4)=36

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Solution for (2x+4)(2x+4)=36 equation:


Simplifying
(2x + 4)(2x + 4) = 36

Reorder the terms:
(4 + 2x)(2x + 4) = 36

Reorder the terms:
(4 + 2x)(4 + 2x) = 36

Multiply (4 + 2x) * (4 + 2x)
(4(4 + 2x) + 2x * (4 + 2x)) = 36
((4 * 4 + 2x * 4) + 2x * (4 + 2x)) = 36
((16 + 8x) + 2x * (4 + 2x)) = 36
(16 + 8x + (4 * 2x + 2x * 2x)) = 36
(16 + 8x + (8x + 4x2)) = 36

Combine like terms: 8x + 8x = 16x
(16 + 16x + 4x2) = 36

Solving
16 + 16x + 4x2 = 36

Solving for variable 'x'.

Reorder the terms:
16 + -36 + 16x + 4x2 = 36 + -36

Combine like terms: 16 + -36 = -20
-20 + 16x + 4x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-20 + 16x + 4x2 = 0

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

Factor a trinomial.
4((-5 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

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

Solution

x = {-5, 1}

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