x^2-4x+4=2x^2-7x-14

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Solution for x^2-4x+4=2x^2-7x-14 equation:


Simplifying
x2 + -4x + 4 = 2x2 + -7x + -14

Reorder the terms:
4 + -4x + x2 = 2x2 + -7x + -14

Reorder the terms:
4 + -4x + x2 = -14 + -7x + 2x2

Solving
4 + -4x + x2 = -14 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + 14 + -4x + 7x + x2 + -2x2 = -14 + -7x + 2x2 + 14 + 7x + -2x2

Combine like terms: 4 + 14 = 18
18 + -4x + 7x + x2 + -2x2 = -14 + -7x + 2x2 + 14 + 7x + -2x2

Combine like terms: -4x + 7x = 3x
18 + 3x + x2 + -2x2 = -14 + -7x + 2x2 + 14 + 7x + -2x2

Combine like terms: x2 + -2x2 = -1x2
18 + 3x + -1x2 = -14 + -7x + 2x2 + 14 + 7x + -2x2

Reorder the terms:
18 + 3x + -1x2 = -14 + 14 + -7x + 7x + 2x2 + -2x2

Combine like terms: -14 + 14 = 0
18 + 3x + -1x2 = 0 + -7x + 7x + 2x2 + -2x2
18 + 3x + -1x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
18 + 3x + -1x2 = 0 + 2x2 + -2x2
18 + 3x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
18 + 3x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(3 + x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {6, -3}

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