5x^2+10x+5=180

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Solution for 5x^2+10x+5=180 equation:


Simplifying
5x2 + 10x + 5 = 180

Reorder the terms:
5 + 10x + 5x2 = 180

Solving
5 + 10x + 5x2 = 180

Solving for variable 'x'.

Reorder the terms:
5 + -180 + 10x + 5x2 = 180 + -180

Combine like terms: 5 + -180 = -175
-175 + 10x + 5x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-175 + 10x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-35 + 2x + x2) = 0

Factor a trinomial.
5((-7 + -1x)(5 + -1x)) = 0

Ignore the factor 5.

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 '(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 = {-7, 5}

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