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

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


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

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

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

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

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

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

Solving
-8 + 2x + x2 = -2 + 7x

Solving for variable 'x'.

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

Combine like terms: -8 + 2 = -6
-6 + 2x + -7x + x2 = -2 + 7x + 2 + -7x

Combine like terms: 2x + -7x = -5x
-6 + -5x + x2 = -2 + 7x + 2 + -7x

Reorder the terms:
-6 + -5x + x2 = -2 + 2 + 7x + -7x

Combine like terms: -2 + 2 = 0
-6 + -5x + x2 = 0 + 7x + -7x
-6 + -5x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-6 + -5x + x2 = 0

Factor a trinomial.
(-1 + -1x)(6 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-1, 6}

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