(x+4)(x-2)=7

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Solution for (x+4)(x-2)=7 equation:


Simplifying
(x + 4)(x + -2) = 7

Reorder the terms:
(4 + x)(x + -2) = 7

Reorder the terms:
(4 + x)(-2 + x) = 7

Multiply (4 + x) * (-2 + x)
(4(-2 + x) + x(-2 + x)) = 7
((-2 * 4 + x * 4) + x(-2 + x)) = 7
((-8 + 4x) + x(-2 + x)) = 7
(-8 + 4x + (-2 * x + x * x)) = 7
(-8 + 4x + (-2x + x2)) = 7

Combine like terms: 4x + -2x = 2x
(-8 + 2x + x2) = 7

Solving
-8 + 2x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-8 + -7 + 2x + x2 = 7 + -7

Combine like terms: -8 + -7 = -15
-15 + 2x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-15 + 2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(3 + -1x) = 0

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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-5, 3}

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