5x^2+5x-8=4x^2+7x+7

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Solution for 5x^2+5x-8=4x^2+7x+7 equation: 


Simplifying
5x2 + 5x + -8 = 4x2 + 7x + 7

Reorder the terms:
-8 + 5x + 5x2 = 4x2 + 7x + 7

Reorder the terms:
-8 + 5x + 5x2 = 7 + 7x + 4x2

Solving
-8 + 5x + 5x2 = 7 + 7x + 4x2

Solving for variable 'x'.

Reorder the terms:
-8 + -7 + 5x + -7x + 5x2 + -4x2 = 7 + 7x + 4x2 + -7 + -7x + -4x2

Combine like terms: -8 + -7 = -15
-15 + 5x + -7x + 5x2 + -4x2 = 7 + 7x + 4x2 + -7 + -7x + -4x2

Combine like terms: 5x + -7x = -2x
-15 + -2x + 5x2 + -4x2 = 7 + 7x + 4x2 + -7 + -7x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-15 + -2x + 1x2 = 7 + 7x + 4x2 + -7 + -7x + -4x2

Reorder the terms:
-15 + -2x + 1x2 = 7 + -7 + 7x + -7x + 4x2 + -4x2

Combine like terms: 7 + -7 = 0
-15 + -2x + 1x2 = 0 + 7x + -7x + 4x2 + -4x2
-15 + -2x + 1x2 = 7x + -7x + 4x2 + -4x2

Combine like terms: 7x + -7x = 0
-15 + -2x + 1x2 = 0 + 4x2 + -4x2
-15 + -2x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-15 + -2x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}

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