2x^2-68=10(x+10)

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Solution for 2x^2-68=10(x+10) equation: 


Simplifying
2x2 + -68 = 10(x + 10)

Reorder the terms:
-68 + 2x2 = 10(x + 10)

Reorder the terms:
-68 + 2x2 = 10(10 + x)
-68 + 2x2 = (10 * 10 + x * 10)
-68 + 2x2 = (100 + 10x)

Solving
-68 + 2x2 = 100 + 10x

Solving for variable 'x'.

Reorder the terms:
-68 + -100 + -10x + 2x2 = 100 + 10x + -100 + -10x

Combine like terms: -68 + -100 = -168
-168 + -10x + 2x2 = 100 + 10x + -100 + -10x

Reorder the terms:
-168 + -10x + 2x2 = 100 + -100 + 10x + -10x

Combine like terms: 100 + -100 = 0
-168 + -10x + 2x2 = 0 + 10x + -10x
-168 + -10x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-168 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-84 + -5x + x2) = 0

Factor a trinomial.
2((-7 + -1x)(12 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-7, 12}

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