7x^2+7x-6=12-8x

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Solution for 7x^2+7x-6=12-8x equation:


Simplifying
7x2 + 7x + -6 = 12 + -8x

Reorder the terms:
-6 + 7x + 7x2 = 12 + -8x

Solving
-6 + 7x + 7x2 = 12 + -8x

Solving for variable 'x'.

Reorder the terms:
-6 + -12 + 7x + 8x + 7x2 = 12 + -8x + -12 + 8x

Combine like terms: -6 + -12 = -18
-18 + 7x + 8x + 7x2 = 12 + -8x + -12 + 8x

Combine like terms: 7x + 8x = 15x
-18 + 15x + 7x2 = 12 + -8x + -12 + 8x

Reorder the terms:
-18 + 15x + 7x2 = 12 + -12 + -8x + 8x

Combine like terms: 12 + -12 = 0
-18 + 15x + 7x2 = 0 + -8x + 8x
-18 + 15x + 7x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-18 + 15x + 7x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -7x) = 0

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(6 + -7x)' equal to zero and attempt to solve: Simplifying 6 + -7x = 0 Solving 6 + -7x = 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 + -7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x = 0 + -6 -7x = 0 + -6 Combine like terms: 0 + -6 = -6 -7x = -6 Divide each side by '-7'. x = 0.8571428571 Simplifying x = 0.8571428571

Solution

x = {-3, 0.8571428571}

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