4x(x+8)-4=34-2x

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Solution for 4x(x+8)-4=34-2x equation:


Simplifying
4x(x + 8) + -4 = 34 + -2x

Reorder the terms:
4x(8 + x) + -4 = 34 + -2x
(8 * 4x + x * 4x) + -4 = 34 + -2x
(32x + 4x2) + -4 = 34 + -2x

Reorder the terms:
-4 + 32x + 4x2 = 34 + -2x

Solving
-4 + 32x + 4x2 = 34 + -2x

Solving for variable 'x'.

Reorder the terms:
-4 + -34 + 32x + 2x + 4x2 = 34 + -2x + -34 + 2x

Combine like terms: -4 + -34 = -38
-38 + 32x + 2x + 4x2 = 34 + -2x + -34 + 2x

Combine like terms: 32x + 2x = 34x
-38 + 34x + 4x2 = 34 + -2x + -34 + 2x

Reorder the terms:
-38 + 34x + 4x2 = 34 + -34 + -2x + 2x

Combine like terms: 34 + -34 = 0
-38 + 34x + 4x2 = 0 + -2x + 2x
-38 + 34x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-38 + 34x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 17x + 2x2) = 0

Factor a trinomial.
2((-19 + -2x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-19 + -2x)' equal to zero and attempt to solve: Simplifying -19 + -2x = 0 Solving -19 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -2x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2x = 0 + 19 -2x = 0 + 19 Combine like terms: 0 + 19 = 19 -2x = 19 Divide each side by '-2'. x = -9.5 Simplifying x = -9.5

Subproblem 2

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

Solution

x = {-9.5, 1}

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