4x^2+28x+760=1000

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Solution for 4x^2+28x+760=1000 equation:


Simplifying
4x2 + 28x + 760 = 1000

Reorder the terms:
760 + 28x + 4x2 = 1000

Solving
760 + 28x + 4x2 = 1000

Solving for variable 'x'.

Reorder the terms:
760 + -1000 + 28x + 4x2 = 1000 + -1000

Combine like terms: 760 + -1000 = -240
-240 + 28x + 4x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-240 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-60 + 7x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12

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 = {-12, 5}

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