(50+2x)(30+2x)-1500=425

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Solution for (50+2x)(30+2x)-1500=425 equation:


Simplifying
(50 + 2x)(30 + 2x) + -1500 = 425

Multiply (50 + 2x) * (30 + 2x)
(50(30 + 2x) + 2x * (30 + 2x)) + -1500 = 425
((30 * 50 + 2x * 50) + 2x * (30 + 2x)) + -1500 = 425
((1500 + 100x) + 2x * (30 + 2x)) + -1500 = 425
(1500 + 100x + (30 * 2x + 2x * 2x)) + -1500 = 425
(1500 + 100x + (60x + 4x2)) + -1500 = 425

Combine like terms: 100x + 60x = 160x
(1500 + 160x + 4x2) + -1500 = 425

Reorder the terms:
1500 + -1500 + 160x + 4x2 = 425

Combine like terms: 1500 + -1500 = 0
0 + 160x + 4x2 = 425
160x + 4x2 = 425

Solving
160x + 4x2 = 425

Solving for variable 'x'.

Reorder the terms:
-425 + 160x + 4x2 = 425 + -425

Combine like terms: 425 + -425 = 0
-425 + 160x + 4x2 = 0

Factor a trinomial.
(-85 + -2x)(5 + -2x) = 0

Subproblem 1

Set the factor '(-85 + -2x)' equal to zero and attempt to solve: Simplifying -85 + -2x = 0 Solving -85 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + -2x = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -2x = 0 + 85 -2x = 0 + 85 Combine like terms: 0 + 85 = 85 -2x = 85 Divide each side by '-2'. x = -42.5 Simplifying x = -42.5

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-42.5, 2.5}

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