Solve 12(x)^(3)+4(x)^(2)+3x+8-y=16(x)^(3)-6(x)^(2)+5x+11 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$12 { x }^{ 3 } +4 { x }^{ 2 } +3x+8-y=16 { x }^{ 3 } -6 { x }^{ 2 } +5x+11$$

Solve for y

$y=-4x^{3}+10x^{2}-2x-3$

Steps for Solving Linear Equation

Subtract $12x^{3}$ from both sides.

$$4x^{2}+3x+8-y=16x^{3}-6x^{2}+5x+11-12x^{3}$$

Combine $16x^{3}$ and $-12x^{3}$ to get $4x^{3}$.

$$4x^{2}+3x+8-y=4x^{3}-6x^{2}+5x+11$$

Subtract $4x^{2}$ from both sides.

$$3x+8-y=4x^{3}-6x^{2}+5x+11-4x^{2}$$

Combine $-6x^{2}$ and $-4x^{2}$ to get $-10x^{2}$.

$$3x+8-y=4x^{3}-10x^{2}+5x+11$$

Subtract $3x$ from both sides.

$$8-y=4x^{3}-10x^{2}+5x+11-3x$$

Combine $5x$ and $-3x$ to get $2x$.

$$8-y=4x^{3}-10x^{2}+2x+11$$

Subtract $8$ from both sides.

$$-y=4x^{3}-10x^{2}+2x+11-8$$

Subtract $8$ from $11$ to get $3$.

$$-y=4x^{3}-10x^{2}+2x+3$$

Divide both sides by $-1$.

$$\frac{-y}{-1}=\frac{4x^{3}-10x^{2}+2x+3}{-1}$$

Dividing by $-1$ undoes the multiplication by $-1$.

$$y=\frac{4x^{3}-10x^{2}+2x+3}{-1}$$

Divide $4x^{3}-10x^{2}+2x+3$ by $-1$.

$$y=-4x^{3}+10x^{2}-2x-3$$