4x(x+4)=84

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Solution for 4x(x+4)=84 equation:


Simplifying
4x(x + 4) = 84

Reorder the terms:
4x(4 + x) = 84
(4 * 4x + x * 4x) = 84
(16x + 4x2) = 84

Solving
16x + 4x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + 16x + 4x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + 4x + x2) = 0

Factor a trinomial.
4((-7 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-7, 3}

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