5(x^2-1)=3(x+29)

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Solution for 5(x^2-1)=3(x+29) equation: 


Simplifying
5(x2 + -1) = 3(x + 29)

Reorder the terms:
5(-1 + x2) = 3(x + 29)
(-1 * 5 + x2 * 5) = 3(x + 29)
(-5 + 5x2) = 3(x + 29)

Reorder the terms:
-5 + 5x2 = 3(29 + x)
-5 + 5x2 = (29 * 3 + x * 3)
-5 + 5x2 = (87 + 3x)

Solving
-5 + 5x2 = 87 + 3x

Solving for variable 'x'.

Reorder the terms:
-5 + -87 + -3x + 5x2 = 87 + 3x + -87 + -3x

Combine like terms: -5 + -87 = -92
-92 + -3x + 5x2 = 87 + 3x + -87 + -3x

Reorder the terms:
-92 + -3x + 5x2 = 87 + -87 + 3x + -3x

Combine like terms: 87 + -87 = 0
-92 + -3x + 5x2 = 0 + 3x + -3x
-92 + -3x + 5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-92 + -3x + 5x2 = 0

Factor a trinomial.
(-4 + -1x)(23 + -5x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(23 + -5x)' equal to zero and attempt to solve:

Simplifying
23 + -5x = 0

Solving
23 + -5x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -5x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -5x = 0 + -23
-5x = 0 + -23

Combine like terms: 0 + -23 = -23
-5x = -23

Divide each side by '-5'.
x = 4.6

Simplifying
x = 4.6
Solution
x = {-4, 4.6}

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