0=x^2+4x-32

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Solution for 0=x^2+4x-32 equation:


Simplifying
0 = x2 + 4x + -32

Reorder the terms:
0 = -32 + 4x + x2

Solving
0 = -32 + 4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 32 = 32
32 + -4x + -1x2 = -32 + 4x + x2 + 32 + -4x + -1x2

Reorder the terms:
32 + -4x + -1x2 = -32 + 32 + 4x + -4x + x2 + -1x2

Combine like terms: -32 + 32 = 0
32 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
32 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
32 + -4x + -1x2 = 0 + x2 + -1x2
32 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
32 + -4x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(8 + x) = 0

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8

Solution

x = {4, -8}

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