5(x^2+4)-3=4(x^2-2x)+26

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Solution for 5(x^2+4)-3=4(x^2-2x)+26 equation:


Simplifying
5(x2 + 4) + -3 = 4(x2 + -2x) + 26

Reorder the terms:
5(4 + x2) + -3 = 4(x2 + -2x) + 26
(4 * 5 + x2 * 5) + -3 = 4(x2 + -2x) + 26
(20 + 5x2) + -3 = 4(x2 + -2x) + 26

Reorder the terms:
20 + -3 + 5x2 = 4(x2 + -2x) + 26

Combine like terms: 20 + -3 = 17
17 + 5x2 = 4(x2 + -2x) + 26

Reorder the terms:
17 + 5x2 = 4(-2x + x2) + 26
17 + 5x2 = (-2x * 4 + x2 * 4) + 26
17 + 5x2 = (-8x + 4x2) + 26

Reorder the terms:
17 + 5x2 = 26 + -8x + 4x2

Solving
17 + 5x2 = 26 + -8x + 4x2

Solving for variable 'x'.

Reorder the terms:
17 + -26 + 8x + 5x2 + -4x2 = 26 + -8x + 4x2 + -26 + 8x + -4x2

Combine like terms: 17 + -26 = -9
-9 + 8x + 5x2 + -4x2 = 26 + -8x + 4x2 + -26 + 8x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-9 + 8x + 1x2 = 26 + -8x + 4x2 + -26 + 8x + -4x2

Reorder the terms:
-9 + 8x + 1x2 = 26 + -26 + -8x + 8x + 4x2 + -4x2

Combine like terms: 26 + -26 = 0
-9 + 8x + 1x2 = 0 + -8x + 8x + 4x2 + -4x2
-9 + 8x + 1x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
-9 + 8x + 1x2 = 0 + 4x2 + -4x2
-9 + 8x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-9 + 8x + 1x2 = 0

Factor a trinomial.
(-9 + -1x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

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

Solution

x = {-9, 1}

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