5(x^2+x-1)=7-8x-9x^2

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Solution for 5(x^2+x-1)=7-8x-9x^2 equation: 


Simplifying
5(x2 + x + -1) = 7 + -8x + -9x2

Reorder the terms:
5(-1 + x + x2) = 7 + -8x + -9x2
(-1 * 5 + x * 5 + x2 * 5) = 7 + -8x + -9x2
(-5 + 5x + 5x2) = 7 + -8x + -9x2

Solving
-5 + 5x + 5x2 = 7 + -8x + -9x2

Solving for variable 'x'.

Reorder the terms:
-5 + -7 + 5x + 8x + 5x2 + 9x2 = 7 + -8x + -9x2 + -7 + 8x + 9x2

Combine like terms: -5 + -7 = -12
-12 + 5x + 8x + 5x2 + 9x2 = 7 + -8x + -9x2 + -7 + 8x + 9x2

Combine like terms: 5x + 8x = 13x
-12 + 13x + 5x2 + 9x2 = 7 + -8x + -9x2 + -7 + 8x + 9x2

Combine like terms: 5x2 + 9x2 = 14x2
-12 + 13x + 14x2 = 7 + -8x + -9x2 + -7 + 8x + 9x2

Reorder the terms:
-12 + 13x + 14x2 = 7 + -7 + -8x + 8x + -9x2 + 9x2

Combine like terms: 7 + -7 = 0
-12 + 13x + 14x2 = 0 + -8x + 8x + -9x2 + 9x2
-12 + 13x + 14x2 = -8x + 8x + -9x2 + 9x2

Combine like terms: -8x + 8x = 0
-12 + 13x + 14x2 = 0 + -9x2 + 9x2
-12 + 13x + 14x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-12 + 13x + 14x2 = 0

Factor a trinomial.
(-3 + -2x)(4 + -7x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(4 + -7x)' equal to zero and attempt to solve:

Simplifying
4 + -7x = 0

Solving
4 + -7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = 0 + -4
-7x = 0 + -4

Combine like terms: 0 + -4 = -4
-7x = -4

Divide each side by '-7'.
x = 0.5714285714

Simplifying
x = 0.5714285714
Solution
x = {-1.5, 0.5714285714}

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