(x+2)(2x-3)=x+26

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Solution for (x+2)(2x-3)=x+26 equation:


Simplifying
(x + 2)(2x + -3) = x + 26

Reorder the terms:
(2 + x)(2x + -3) = x + 26

Reorder the terms:
(2 + x)(-3 + 2x) = x + 26

Multiply (2 + x) * (-3 + 2x)
(2(-3 + 2x) + x(-3 + 2x)) = x + 26
((-3 * 2 + 2x * 2) + x(-3 + 2x)) = x + 26
((-6 + 4x) + x(-3 + 2x)) = x + 26
(-6 + 4x + (-3 * x + 2x * x)) = x + 26
(-6 + 4x + (-3x + 2x2)) = x + 26

Combine like terms: 4x + -3x = 1x
(-6 + 1x + 2x2) = x + 26

Reorder the terms:
-6 + 1x + 2x2 = 26 + x

Solving
-6 + 1x + 2x2 = 26 + x

Solving for variable 'x'.

Reorder the terms:
-6 + -26 + 1x + -1x + 2x2 = 26 + x + -26 + -1x

Combine like terms: -6 + -26 = -32
-32 + 1x + -1x + 2x2 = 26 + x + -26 + -1x

Combine like terms: 1x + -1x = 0
-32 + 0 + 2x2 = 26 + x + -26 + -1x
-32 + 2x2 = 26 + x + -26 + -1x

Reorder the terms:
-32 + 2x2 = 26 + -26 + x + -1x

Combine like terms: 26 + -26 = 0
-32 + 2x2 = 0 + x + -1x
-32 + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-32 + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + x2) = 0

Factor a difference between two squares.
2((4 + x)(-4 + x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4

Solution

x = {-4, 4}

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