4x^2=16x-16

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Solution for 4x^2=16x-16 equation:


Simplifying
4x2 = 16x + -16

Reorder the terms:
4x2 = -16 + 16x

Solving
4x2 = -16 + 16x

Solving for variable 'x'.

Reorder the terms:
16 + -16x + 4x2 = -16 + 16x + 16 + -16x

Reorder the terms:
16 + -16x + 4x2 = -16 + 16 + 16x + -16x

Combine like terms: -16 + 16 = 0
16 + -16x + 4x2 = 0 + 16x + -16x
16 + -16x + 4x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
16 + -16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -4x + x2) = 0

Factor a trinomial.
4((2 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

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 '(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

Solution

x = {2, 2}

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