(x-4)(2x+3)-(8+x)=

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Solution for (x-4)(2x+3)-(8+x)= equation:


Simplifying
(x + -4)(2x + 3) + -1(8 + x) = 0

Reorder the terms:
(-4 + x)(2x + 3) + -1(8 + x) = 0

Reorder the terms:
(-4 + x)(3 + 2x) + -1(8 + x) = 0

Multiply (-4 + x) * (3 + 2x)
(-4(3 + 2x) + x(3 + 2x)) + -1(8 + x) = 0
((3 * -4 + 2x * -4) + x(3 + 2x)) + -1(8 + x) = 0
((-12 + -8x) + x(3 + 2x)) + -1(8 + x) = 0
(-12 + -8x + (3 * x + 2x * x)) + -1(8 + x) = 0
(-12 + -8x + (3x + 2x2)) + -1(8 + x) = 0

Combine like terms: -8x + 3x = -5x
(-12 + -5x + 2x2) + -1(8 + x) = 0
-12 + -5x + 2x2 + (8 * -1 + x * -1) = 0
-12 + -5x + 2x2 + (-8 + -1x) = 0

Reorder the terms:
-12 + -8 + -5x + -1x + 2x2 = 0

Combine like terms: -12 + -8 = -20
-20 + -5x + -1x + 2x2 = 0

Combine like terms: -5x + -1x = -6x
-20 + -6x + 2x2 = 0

Solving
-20 + -6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -3x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

x = {-2, 5}

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