5(x^2-1)=15(2x-2)

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Solution for 5(x^2-1)=15(2x-2) equation: 


Simplifying
5(x2 + -1) = 15(2x + -2)

Reorder the terms:
5(-1 + x2) = 15(2x + -2)
(-1 * 5 + x2 * 5) = 15(2x + -2)
(-5 + 5x2) = 15(2x + -2)

Reorder the terms:
-5 + 5x2 = 15(-2 + 2x)
-5 + 5x2 = (-2 * 15 + 2x * 15)
-5 + 5x2 = (-30 + 30x)

Solving
-5 + 5x2 = -30 + 30x

Solving for variable 'x'.

Reorder the terms:
-5 + 30 + -30x + 5x2 = -30 + 30x + 30 + -30x

Combine like terms: -5 + 30 = 25
25 + -30x + 5x2 = -30 + 30x + 30 + -30x

Reorder the terms:
25 + -30x + 5x2 = -30 + 30 + 30x + -30x

Combine like terms: -30 + 30 = 0
25 + -30x + 5x2 = 0 + 30x + -30x
25 + -30x + 5x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
25 + -30x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -6x + x2) = 0

Factor a trinomial.
5((1 + -1x)(5 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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 = {1, 5}

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